The equipotential surfaces of cubic lattices

The areas of zero electrostatic potential within an array of electric charges in an ionic crystal can be represented as a zero equipotential surface (ZEPS), which separates space into domains of positive and negative potential. ZEPS are conventionally expressed in terms of nodal surfaces. We express the coordinates and charge distribution of several ZEPS in terms of the Jacobi theta functions, and provide their graphical visualisation.